微分的

In this paper,we build symplectic structure of 2-nd order and high order singular differential operators on infinite interval, we construct a symplectic space by the maximal and minimal operator domain .

本文研究了无穷区间上二阶、高阶奇型微分算子的辛结构，利用最大与最小算子域构造了一个辛空间，用辛空间中的线性流形来刻画定义在无穷区间上二阶、高阶奇型对称微分算子的自共轭扩张问题。

This course mainly contents real number muster and function, limit of number sequence, limit of function, continuity, derived number and differential, differential mean value theorem and its application, completeness of real number, integral, series(including positive series and Fourier series), multiple- differential, double integral, integral with parameter, curve integral, camber integral and so on.

理解和掌握《数学分析》的概念、理论和方法，对于学生加深理解数学的基本思想和方法，培养抽象思维能力和逻辑思维能力，提高数学素养具有重要的意义。主要内容包括：实数集和函数，数列极限，函数极限，连续性，导数和微分，微分中值定理及其应用，实数完备性，积分、级数(包括幂级数、Fourier级数)、多元微分学、重积分、含参变量积分、曲线积分、曲面积分等。

The last part is concerned with the nonoscillatory problems of odd-dimentional systems of linear retarded functional differential equa-tions.

第四章研究了一类奇数维分布型线性泛函微分系统的非振动性。同时也给出了相应的中立型分布型线性泛函微分系统的非振动性。

By transforming high - grade gentle lack one type linear differential equation into the linear differential equation of successive integral, the theory and method for the general solutions of this kind of equation are determined.

方程'+=f是高阶线性微分方程，(约定尹0)=刃，是两项和的形式，其特征是含有相同的底，导数的次数相差一阶，因此不妨定义该方程为：高阶和式次数差一型线性微分方程。

In the chapter 3,we base on the existence of periodic solution ,using the method of linearization and applying the mean value theorem and the variation-of-constants formula, we get the sufficient condition of the exponential stability of periodic solution of a class of nonlinear functional differential system .

在第三章中，建立在系统周期解存在的基础上，利用线性化的方法，根据微分中值定理和常量变差公式，得到了一类非线性泛函微分系统周期解指数稳定的充分条件。

Two-point boundary value problems of second order mixed type integro-differential-difference equation is studied by means of differential inequality theories.

利用微分不等式技巧研究了某一类二阶混合型积分微分差分方程的两点边值问题，在上下解存在的条件下，得到了解的存在性和唯一性定理。

Firstly, the structure equations of the evolution surface family are derived, and some laws of the surface invariants evolution are obtained, based on modern differential geometry, especially, differential forms and frame field theory.

本文以微分形式、活动标架为工具，推导出演化曲面、曲线的结构方程，并重点研究曲面微分不变量、不变式、整不变量及标架的演化规律，给出了这些规律同演化速率函数之间的关系。

In Chapter Ⅲ, by considering functions H k that may not have nonpositive partial derivative on s and employing integral averaging technique and Hardy inequality, the oscillation for a class of high order nonlinear differential equations and high order nonlinear damped differential equations is discussed, new oscillation criteria are established.

第二章利用广义Riccati技巧、积分平均技巧以及微分不等式理论，讨论了一类二阶非线性常微分方程的振动性，得到了若干新的振动准则，并讨论了该方程具有强迫项时解的渐近性态。

Of the fundamental matrix in (2) satisfies the differential equation =A , it follows that the matrix = itself satisfies the matrix differential equation Because its column vectors are linearly independent, it also follows that the fundamental matrix is nonsingular, and therefore has inverse matrix .

基本矩阵的求解由于（2）中的基本矩阵的列向量满足微分方程A，进而这个矩阵本身就满足矩阵微分方程。

Which is one of the most important in the research of ordinary differential equation.

常微分方程解的有界性问题最早是在研究生物学，生态学，生理学，物理学，神经网络等问题中提出的，是常微分方程研究中一个十分重要的领域。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷